Resonating valence bond wavefunctions and classical interacting dimer models

Abstract

We relate properties of nearest-neighbour resonating valence bond (nnRVB) wavefunctions for $SU(g)$ spin systems on two dimensional bipartite lattices to those of fully-packed classical dimer models with potential energy $V$ on the same lattice. We define a cluster expansion of $V$ in terms of $n$-body potentials $V_n$, which are recursively determined from the nnRVB wavefunction on {\em finite subgraphs} of the original lattice. The magnitude of the $n$-body interaction $V_n$ ($n>1$) is of order $\mathcal{O}(g^{-(n-1)})$ for small $g^{-1}$, while $V_1$ reduces to a constant due to the fully-packed nature of the model. At leading non-trivial order on the square lattice, the interacting dimer model only has two-body interactions $V_2(g)$ that favour two parallel dimers on elementary plaquettes. Setting $g=2$ and using the results of earlier work on this interacting dimer model, we find that the long-distance behaviour of the bond-energy correlation function is dominated by an oscillatory term that decays as $1/|\vec{r}{|}^{\alpha }$ with $\alpha \approx 1.22$ for SU(2) spins. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wavefunction, which give $\alpha \approx 1.20$.

4+ pages, 2-column format, 1 figure

References in corpus (7)

• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Some formal results for the valence bond basis
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet

Cited by in corpus (18)

• Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers
• Entanglement in gapless resonating valence bond states
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Correlated valence-bond states
• Resonating valence-bond physics on the honeycomb lattice
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Interacting double dimer model on the square lattice
• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
• SU(4) topological RVB spin liquid on the square lattice
• Height fluctuations in non-integrable classical dimers
• Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model
• Synchronization transition in the double dimer model on the cubic lattice
• A Statistical Model of Current Loops and Magnetic Monopoles
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models